Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains

Abstract

The Ricci curvature of the Bergman metric on a bounded domain $D\subset {\mathbb{C}}^n$ is strictly bounded above by $n+1$ and consequently $\log (K_D^{n+1}{g}_{B,D})$, where $K_D$ is the Bergman kernel for $D$ on the diagonal and $g_{B,D}$ is the Riemannian volume element of the Bergman metric on $D$, is the potential for a Kähler metric on $D$ known as the Kobayashi--Fuks metric. In this note we study the localization of this metric near holomorphic peak points and also show that this metric shares several properties with the Bergman metric on strongly pseudoconvex domains.

23 pages

Cited by in corpus (2)

• Existence of geodesic spirals for the Kobayashi--Fuks metric on planar domains
• Weighted boundary limits of the Kobayashi--Fuks metric on h-extendible domains